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Article
Astronomy & Astrophysics
Naying Zhou et al.
Summary: Recent publications have shown that explicit symplectic integrators for Schwarzschild and Kerr-type spacetimes, based on splitting and composition methods, offer significant advantages in accuracy. Among these methods, optimized fourth-order partitioned Runge-Kutta and Runge-Kutta-Nystrom methods demonstrate the best performance.
ASTROPHYSICAL JOURNAL
(2022)
Article
Mathematics, Applied
Buddhika Jayawardana et al.
Summary: In this paper, we propose a symplectic integrator for non-separable Hamilton-ian systems, which combines the extended phase space approach of Pihajoki and the symmetric projection method. Our method is semiexplicit, with an explicit main time evolution step and an implicit symmetric projection step, and it preserves symplecticity in the original phase space.
MATHEMATICS OF COMPUTATION
(2022)
Article
Astronomy & Astrophysics
Xin Wu et al.
Summary: Many Hamiltonian problems in the solar system can be separated into two parts, allowing for the development and application of explicit symplectic integrators. However, this approach is not applicable to curved spacetimes in general relativity and modified theories of gravity. Recent advancements have shown that certain black hole spacetimes can be used to construct explicit symplectic integrators. Although other curved spacetimes do not have this property, their corresponding time-transformation Hamiltonians do. In this study, explicit symplectic schemes are developed for curved spacetimes, introducing a class of spacetimes with directly separable Hamiltonians and presenting spacetimes with time-transformation Hamiltonians that have desired splits.
ASTROPHYSICAL JOURNAL
(2022)
Article
Astronomy & Astrophysics
Ying Wang et al.
Summary: This study explored the possibility of constructing explicit symplectic integrators for a Hamiltonian of charged particles moving around a Reissner-Nordstrom black hole with an external magnetic field. The proposed algorithms showed desirable properties in their long-term stability, precision, and efficiency for appropriate choices of step size. Effects of black hole's charge, Coulomb part of electromagnetic potential, and magnetic parameter on the dynamical behavior were investigated.
ASTROPHYSICAL JOURNAL
(2021)
Article
Astronomy & Astrophysics
Ying Wang et al.
Summary: The study proposes a method to split the Hamiltonian into six analytically solvable pieces for describing the motion of charged particles around the Reissner-Nordstrom-(anti)-de Sitter black hole. The second- and fourth-order explicit symplectic integrators show excellent long-term behavior in maintaining the boundness of Hamiltonian errors with appropriate step sizes. An increase in the positive cosmological constant leads to stronger chaos in the global phase space, while an increase in the negative cosmological constant does not. This difference is due to the role of the cosmological constant as either a repulsive or attractive force in different black hole configurations.
ASTROPHYSICAL JOURNAL SUPPLEMENT SERIES
(2021)
Article
Astronomy & Astrophysics
Xin Wu et al.
Summary: This paper introduces a time transformation method for Kerr geometry, resulting in a time-transformed Hamiltonian with five splitting parts, whose analytical solutions are explicit functions of the new coordinate time. This approach effectively implements new explicit symplectic algorithms with good long-term behavior and high computational efficiency.
ASTROPHYSICAL JOURNAL
(2021)
Article
Astronomy & Astrophysics
Guifan Pan et al.
Summary: The study focused on coherent or exact equations of motion for a conservative post-Newtonian Lagrangian formalism, establishing extended phase-space symplectic-like integrators, and solving velocities iteratively during numerical integration. Using the extended phase-space method, the effects of parameters and initial conditions on orbital dynamics were studied for a post-Newtonian circular restricted three-body problem, as well as for spinning compact binaries, showing superior computational efficiency compared to traditional integrators.
Article
Astronomy & Astrophysics
Ying Wang et al.
Summary: Symplectic integrators that preserve the geometric structure of Hamiltonian flows and do not exhibit secular growth in energy errors are suitable for long-term integration in N-body Hamiltonian systems, but constructing explicit symplectic algorithms in general relativity can be challenging. Implicit symplectic integrators, such as the midpoint rule, are more applicable in such cases.
ASTROPHYSICAL JOURNAL
(2021)
Article
Astronomy & Astrophysics
Dan Li et al.
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
(2017)
Article
Astronomy & Astrophysics
Junjie Luo et al.
ASTROPHYSICAL JOURNAL
(2017)
Article
Computer Science, Interdisciplinary Applications
Molei Tao
JOURNAL OF COMPUTATIONAL PHYSICS
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Article
Astronomy & Astrophysics
Lei Liu et al.
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
(2016)
Article
Astronomy & Astrophysics
Pauli Pihajoki
CELESTIAL MECHANICS & DYNAMICAL ASTRONOMY
(2015)
Article
Mathematics
J. Colliander et al.
INVENTIONES MATHEMATICAE
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Article
Physics, Fluids & Plasmas
Siu A. Chin
Article
Computer Science, Software Engineering
RI McLachlan et al.
BIT NUMERICAL MATHEMATICS
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Article
Physics, Fluids & Plasmas
YK Wu et al.
Article
Physics, Fluids & Plasmas
S Blanes
Article
Chemistry, Physical
JB Sturgeon et al.
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